Explaining coincidences (away)

There’s nothing the Provisional Wing of parapsychology enjoys more than debunking so-called anomalous events by citing the gullibility and scientific illiteracy of we non-parapsychologists. With a wave of the hand, they can explain any event  by citing poor observation and a willingness to believe anything, and investigate no further.

But there is one area of the paranormal that gives the Provos more trouble than any other and against which they have deployed their biggest guns and their most powerful arguments, and that is the realm of coincidences.

Many people have experienced a coincidence that they have found uncanny, astonishing or bewildering, so it is a widespread experience, unlike, say, telepathy. It is one of the few areas of the paranormal that reputable and distinguished scientists have taken an interest in – notably Nobel physics laureate Wolfgang Pauli, and Carl Jung, founder of analytical psychology.

Parapsychologists have deployed two formidable weapons in their quest to prove that there is nothing paranormal about coincidences: the first is a common-sense explanation based on human psychology, the second a mathematical approach. Here I want to take a closer look at both these explanations and to ask if they do in fact rebut Jung’s contention that coincidences may represent paranormal events of some human significance.

The common sense explanation is that we all have a natural tendency to over-estimate the rarity of coincidences. The approach is typified by a TV programme on the paranormal presented by Dr Richard Wiseman and what I might call the case of the Imaginary Air Crashes.

Richard Wiseman is a British version of James “The Amazing” Randi in that he is a professional stage magician turned psychologist and skeptic who sets out to debunk claims of the paranormal. Wiseman is a contributor to the Skeptical Enquirer, the magazine of CSICOP  – the Committee for Scientific Investigation of Claims of the Paranormal. He is currently Professor of the Understanding of Psychology at the University of Hertfordshire. He has debunked both in print and on Television beliefs that he thinks are pseudoscientific.  Yet, like a number of his fellow skeptics, in his eagerness to  debunk the paranormal, he has himself fallen into the trap of employing pseudoscience.

In his TV programme on the paranormal Wiseman  gave details of several seemingly impossible coincidences that had occurred to viewers and gave his explanation of them. Many events, he said, appear to us to be extremely improbable because of our tendency to overestimate their rarity.

For example, he said, someone might have a dream of an air disaster in some foreign country, even seeing the crashed aircraft surrounded by dead bodies. The next day, the dreamer anxiously scans the newspapers and TV and discovers to their amazement that just such an air disaster has occurred. The dreamer believes that he or she has had a premonition and by some paranormal means foresaw the future in detail.

However, Dr Wiseman explained, the real facts are that air travel has become so widespread and there are now so many airlines around the world that air crashes are occurring  practically all the time. Thus what seems an improbable coincidence is in fact very probable. Any time you dream of an airliner crash one is overwhelmingly likely to follow soon after and be misidentified as a rare coincidence.

This explanation is a very persuasive one and also very powerful because it seems intuitively to apply to many other similar cases of “premonition”, “telepathy”, “clairvoyance” and the like, and seems to show both how fallible we are as observers of our own behaviour and how likely we are to be misled by the simplest facts if we haven’t studied them – as scientists like Dr Wiseman have.

There’s just one problem. The very frequent crashes of commercial airline flights that Dr Wiseman blames for this ‘apparent’ precognition don’t exist, except in his skeptic’s imagination.

According to the website maintained by air crash expert Todd Curtis, in 2014, there were 10 commercial airline crashes worldwide in which passengers were injured or killed of which none were in Europe or the United States. The previous year the figure was 7 of which 1 was in the United States and none in Europe.

The kind of crash described by Wisemann, is a rare event, especially in Europe and the U.S. To put these figures into the context of Wiseman’s argument, anyone who dreamed of an air crash in February 2013 had to wait three months for such a crash to occur in April that year  — hardly the stuff of premonitions or significant coincidences.

When a passenger aircraft from a major international airline does crash, especially in Europe (as at Lockerbie) or the US and hits the headlines, it is, as intuition leads us to think, a rare event.  We are not wrong to estimate air crashes as rare — our intuitions are perfectly correct. And “experts” like Dr. Wisemann sometimes make up or select facts to confirm their own prejudices.

The second approach used to debunk coincidences is the mathematical one – calculating with some precision just how probable or improbable certain events are and, once again, showing that some coincidences are much more likely than we might think. One such treatment is the paper by Persi Diaconis, professor of Mathematics at Harvard, and Frederick Mosteller, professor of mathematical statistics emeritus at Harvard.*

The classic example of this mathematical approach – and the one that has become virtually a standard treatment – is that of birthdays. How many people do you have to get together in a room to find that two were born on the same day of the year (though not necessarily the same year)?

The answer is that you have a 50-50 chance of finding two people who share a birthday with as few as 23 people – which seems highly counter-intuitive. If you increase the number of people to 48, you have a 95% chance of finding the birthday ‘twins’, it becomes almost a sure thing.

The same mathematical approach can be used to make seemingly astounding coincidences downright ordinary. Diaconis and Mosteller give an example of a story from the New York Times about a woman in New Jersey who won first prize in the state lottery on two occasions only four months apart. The paper described this as a “1 in 17 trillion” long shot.

The mathematicians say, “The 1 in 17 trillion number is the correct answer to a not very important question. If you buy one ticket for exactly two New Jersey state lotteries, this is the chance both would be winners. (The woman actually purchased multiple tickets repeatedly). “

The important question, they say, is “What is the chance that some person out of the millions and millions of people who buy lottery tickets in the United States, hits a lottery twice in a lifetime? We must remember that many people buy multiple tickets on each of many lotteries.

“Stephen Samuels and George McCabe of the Department of Statistics at Purdue University arrived at some relevant calculations. The called the event ‘practically a sure thing’, calculating that it is better than even odds to have a double winner in seven years someplace in the United States. It is better than 1 in 30 that there is a double winner in a four month period.”

The trouble with the mathematical approach is that the examples have been chosen precisely because it is relatively easy to attribute numerical values to them. But in the real world, the most noteworthy coincidences come in forms that make the mathematical approach impotent as a tool of explanation.

Consider the following coincidence.

Choir practice at the West Side Baptist Church in Beatrice, Nebraska, always began at 7:20 on Wednesday evenings. At 7:25 p.m. on Wednesday, March 1, 1950, an explosion demolished the church. The blast forced a nearby radio station off the air and shattered windows in surrounding homes .but every one of the choir’s fifteen members escaped injury, because all  were late for practice that night, each for their own reasons.

That day, Walter Klempel had gone to the Church to get things ready for choir practice. He lit the furnace as it was a chilly night and the singers would be arriving later at 7:15. He  then went home to dinner. But at 7:10, when it was time for him to go back to the church with his wife and daughter Marilyn, they found that Marilyn’s dress was soiled. They waited while Mrs. Klempel ironed another and so were still at home when the explosion happened.

Ladona Vandergrift, a schoolgirl, was having trouble with her geometry homework. She knew practice began promptly and always came early. But this night she stayed to finish the problem.

Royena Estes was ready on time, but her car would not start. So she and her sister phoned Ladona Vandergrift, and asked her to pick them up. But Ladona was finishing her geometry problem, so the Estes sisters had to wait. Sadie Estes’ story was the same as Royena’s. All day they had been having trouble with the car; it just refused to start.

Mrs. Leonard Schuster would usually have arrived at 7:20 with her small daughter Susan. But on this evening Mrs. Schuster had to go to her mother’s house to help her get ready for another meeting.

Herbert Kipf, a lathe operator, would have been early but had put off an important letter. “I can’t think why,” he said. He stayed to finish writing it and was late.

It was a cold evening. Stenographer Joyce Black, feeling “just plain lazy,” stayed in her warm house until the last possible moment. She was almost ready to leave when the explosion happened.

Because his wife was away, machinist Harvey Ahl was taking care of his two boys. He was going to take them to choir practice with him but somehow he got distracted talking. When he looked at his watch, he saw he was already late.

Marilyn Paul, the choir’s pianist, had planned to arrive half an hour early. However she fell asleep after dinner, and when her mother awakened her at 7:15 she had time only to tidy up and set off.

Mrs. F.E. Paul, choir director and mother of the pianist, was also late because her daughter was. She had tried unsuccessfully to awaken the girl earlier.

High school girls Lucille Jones and Dorothy Wood were neighbors and customarily went to practice together. Lucille was listening to a radio program that didn’t finish until 7:30 and broke her habit of promptness because she wanted to hear the end. Dorothy waited for her.

At 7:25, with a blast heard in almost every corner of Beatrice, the West Side Baptist Church blew up. The walls fell outward, the heavy wooden roof crashed straight down. Anyone inside would have been crushed.  Firemen thought the explosion had been caused by natural gas, which may have leaked into the church from a broken pipe outside and been ignited by the fire in the furnace.

The reason I’ve chosen this particular coincidence is because it  was well documented at the time and has been investigated by myth busters such as Snopes (  http://www.snopes.com/luck/choir.asp ). We have the names of the people involved and their photograph, as well as the report of the fire department who dealt with the explosion. The event undoubtedly happened as described and has not been exaggerated in the telling.

The second reason I’ve chosen this is because it’s not difficult to see the fallacy in the “coincidences are not as rare as you think” explanation and the “Birthday twins” argument.

To try to say something along the lines of  “there is a better than evens chance that somewhere in the United States a church will accidentally explode five minutes after choir practice starts but all fifteen choristers are delayed more than 5 minutes in arriving, in x years” would be ludicrous, because x here must be billions (maybe even billion of billions) of years.

To calculate the probability of this coincidence you would have to take the number of churches that have exploded in the United States (or perhaps in the world) the number of occasions on which the explosion occurred a few minutes after a meeting was due to begin, the number of occasions on which at least fifteen  people who usually attended all failed to attend on the occasion of the explosion for reasons specific to their individual circumstances. You would also include the fact that choristers were rarely late for practice on previous occasions.

You don’t have to be a statistician to see that the odds against all these events coming together at the same moment are so great that it is quite possible this event might occur only once in the lifetime of the planet earth. Yet to all fifteen people involved it was the most significant event in their lives, because all of them came within a whisker of death but survived. To claim that this coincidence is more common that we assume would be idiotic.   So what other scientific explanation is there?

There is something else about it that for me makes the Beatrice explosion stand out. When you have a lot of extraordinary events taking place, such as in wartime, then there are likely to be more extraordinary coincidences than usual. To take an example of a very different kind, hundreds (perhaps thousands) of people fell from aircraft during the second world war without a parachute or with a defective parachute and were killed.

Yet there are two authenticated cases of an airman falling from an aircraft and surviving.  Alan Magee fell 22,000 feet from the rear gun turret of a USAF B17 in 1943, landing on the glass roof of St Nazaire station  Nicholas Alkemade fell 18,000 feet from an RAF Lancaster over Germany in 1944  and survived because of  snow-laden trees and deep drifts of snow breaking his fall.  But as far as I can tell there have been no cases since WWII of anyone surviving a fall from an aircraft. But of course these men would never have been flying bomber aircraft had it not been for the war. And hundreds of others jumped or fell with chutes but died.

The Beatrice church explosion did not take place against a background of heightened action. It was a peacetime accident of a unique kind. There is no surrounding context that could in any way render the event  more probable. The explosion was unpredicted and unpredictable. No warning was issued. Each of the actors in the drama acted on their own initiative or in response to circumstances beyond their control.

In the end, it may, of course, turn out that there is after all nothing remarkable in coincidences and studying them may be a profitless activity. Equally it may well be that Carl Jung was right when he observed that “Some things are not merely irrational, they are beyond reason” and if that is the case then science must find some way of enlarging its method of enquiry to encompass the non-rational, if it wishes to account for everything we find in the world.


*Diaconis, Persi and Mosteller, Frederick, “Methods for studying coincidences” , 1989,Journal of the American Statistical Association, December 1989, Vol 84, No. 408.



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